Trees, forests and jungles: a botanical garden for cluster expansions

Combinatoric formulas for cluster expansions have been improved many times over the years. Here we develop some new combinatoric proofs and extensions of the tree formulas of Brydges and Kennedy, and test them on a series of pedagogical examples.Comment: 37 pages, Ecole Polytechnique A-325.099

Ondelettes and phase cell cluster expansions, a vindication

Y. Meyer has recently developed a particularly useful o.n. basis for L 2 ( R d ). Expansions using this basis, i.e. expansions into “ondelettes” or “wavelets,” have yielded important new results in soft and hard analysis. The expansion into ondelettes of a boson scalar field naturally leads to phase cell cluster expansions, a formalism already developed by the authors using other related bases. Adoption of ondelettes expansions into the phase cell program gives improvements of some extant results, and excises an early error.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46467/1/220_2005_Article_BF01206144.pd

Development and analysis of business models in the South African motor body repair sector

Every enterprise makes use of a business model either explicitly or implicitly. A business model is an abstract of a business plan and is complimentary to the firm’s business strategy. It shows linkages within a business process as it transforms inputs into outputs, and how the enterprise creates and delivers value to its customers. Through a case study research two business models used by South African auto-body repairers were developed and analysed. One is for auto-body repair shops that are recognised by the South African Insurance Association, the panel system, and the other is not. The business models are presented as causal loop diagrams. Design parameters used to describe the architecture were content, structure, governance and complimentaries. These business models were used to explain low margins experienced in this sector. The business model helps small enterprise entrepreneurs, stakeholders in the automotive sector and policy makers to understand the logic of auto-body repair shops

Enhancing competitiveness and enterprise development needs through entrepreneurial skills training for SMEs in the South African Motor Body Repair sector

The aim of this paper is to explore the potential of entrepreneurship education as a leverage tool in enhancing both competitiveness and enterprise development within small and medium enterprises (SMEs) operating in the Motor Body Repair (MBR) sector of the South African automotive industry. An exploratory survey was carried out to ascertain enterprise development needs and competitiveness requirements of these SMEs. The research established that curricula followed in auto body repair training do not consider entrepreneurship education as an important aspect. Major focus of auto body repair training is on repair and replacing of motor vehicle bodywork that would have been damaged in an accident or have suffered from vandalism. The research in addition, established that enterprise development is affected by poor infrastructure, lack of funding, use of poor and old equipment and limited access to markets. Competitive requirements noted were the need for certified multi-skilling training offered by Original Equipment Manufacturers (OEMs) on new vehicle maintenance technologies, acquisition of recommended repair equipment from Original Equipment Suppliers (OES) and the need to integrate entrepreneurship education in the auto body repair curricula. The implications of entrepreneurship education in the auto body repair curriculum would enhance efficient business and financial management, creativity, innovativeness, marketing and job creation opportunities in the MBR sector. For educators’ entrepreneurship education in engineering would prepare students for the ever changing labour markets and encourage them to create new enterprises of their own rather than being perpetual job seekers

Balian-Low Theorems in Several Variables

Recently, Nitzan and Olsen showed that Balian-Low theorems (BLTs) hold for discrete Gabor systems defined on $\mathbb{Z}_d$. Here we extend these results to a multivariable setting. Additionally, we show a variety of applications of the Quantitative BLT, proving in particular nonsymmetric BLTs in both the discrete and continuous setting for functions with more than one argument. Finally, in direct analogy of the continuous setting, we show the Quantitative Finite BLT implies the Finite BLT.Comment: To appear in Approximation Theory 16 conference proceedings volum

Irreducible Hamiltonian approach to the Freedman-Townsend model

The irreducible BRST symmetry for the Freedman-Townsend model is derived. The comparison with the standard reducible approach is also addressed.Comment: 18 pages, LaTeX 2.0

The ne plus ultra of tree graph inequalities

With nary mention of a tree graph, we obtain a cluster expansion bound that includes and vastly generalizes bounds as obtained by extant tree graph inequalities. This includes applications to both two-body and many-body potential situations of the recently obtained ‘new improved tree graph inequalities’ that have led to the ‘extra 1/ N ! factors’. We work in a formalism coupling a discrete set of boson variables, such as occurs in a lattice system in classical statistical mechanics, or in Euclidean quantum field theory. The estimates of this Letter apply to numerical factors as arising in cluster expansions, due to essentially arbitrary sequences of the basic operations: interpolation of the covariance, interpolation of the interaction, and integration by parts. This includes complicated evolutions, such as the repeated use of interpolation to decouple the same variables several times, to ensure higher connectivity for renormalization purposes, in quantum field theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43206/1/11005_2004_Article_BF00429953.pd

A note on cluster expansions, tree graph identities, extra 1/ N ! factors!!!

We draw attention to a new tree graph identity which substantially improves on the usual tree graph method of proving convergence of cluster expansions in statistical mechanics and quantum field theory. We can control expansions that could not be controlled before.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43217/1/11005_2004_Article_BF00420041.pd

BRST-anti-BRST Antifield formalism : The Example of the Freedman-Townsend Model

The general BRST-anti-BRST construction in the framework of the antifield-antibracket formalism is illustrated in the case of the Freedmann-Townsend model.Comment: 16 pages, Latex file, Latex errors corrected, otherwise unchange